Digital Commons Network^™

Domain Decomposition Methods For The Solution Of Multiple Scattering Problems, Michael Pedneault

Dissertations

This presents a Schur complement Domain Decomposition (DD) algorithm for the solution of frequency domain multiple scattering problems. Just as in the classical DD methods,(1) the ensemble of scatterers is enclosed in a domain bounded by an artificial boundary, (2) this domain is subdivided into a collection of nonoverlapping subdomains so that the boundaries of the subdomains do not intersect any of the scatterers, and (3) the solutions of the subproblems are connected via Robin boundary conditions matching on the common interfaces between subdomains. Subdomain Robin-to-Robin maps are used to recast the DD problem as a sparse linear system whose …

Fwer Controlling Procedures In Simultaneous And Selective Inference, Li Yu

Dissertations

With increasing complexity of research objectives in clinical trials, a variety of relatively complex and less intuitive multiple testing procedures (MTPs) have been developed and applied in clinical data analysis. In order to make testing strategies more explicit and intuitive to communicate with non-statisticians, several flexible and powerful graphical approaches have recently been introduced in the literature for developing and visualizing newer MTPs. Nevertheless, some theoretical as well as methodological issues still remain to be fully addressed. This dissertation addresses several important issues arising in graphical approaches and related selective inference problems. It consists of three parts.

In the first …

Numerical Simulation Of Dropped Cylindrical Objects Into Water In Two Dimensions (2d), Yi Zhen

University of New Orleans Theses and Dissertations

The dropped objects are identified as one of the top ten causes of fatalities and serious injuries in the oil and gas industry. It is of importance to understand dynamics of dropped objects under water in order to accurately predict the motion of dropped objects and protect the underwater structures and facilities from being damaged. In this thesis, we study nondimensionalization of dynamic equations of dropped cylindrical objects. Nondimensionalization helps to reduce the number of free parameters, identify the relative size of effects of parameters, and gain a deeper insight of the essential nature of dynamics of dropped cylindrical objects …

Gizmos Computer Simulations In The Mathematics Classroom, Bethany L. Inman

Morehead State Theses and Dissertations

A capstone submitted in partial fulfillment of the requirements for the degree of Doctor of Education in the College of Education at Morehead State University by Bethany L. Inman on December 6, 2018

Control Theory: The Double Pendulum Inverted On A Cart, Ian J P Crowe-Wright

Mathematics & Statistics ETDs

In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the Euler-Lagrange equation for the chosen Lagrangian, giving a second-order nonlinear system. This system can be approximated by a linear first-order system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to …

Invariant Subspaces Of Compact Operators And Related Topics, Weston Mckay Grewe

Mathematics

The invariant subspace problem asks if every bounded linear operator on a Banach space has a nontrivial closed invariant subspace. Per Enflo has shown this is false in general, however it is known that every compact operator has an invariant subspace. The purpose of this project is to explore introductory results in functional analysis. Specifically we are interested in understanding compact operators and the proof that all compact operators on a Hilbert space have an invariant subspace. In the process of doing this we build up many examples and theorems relating to operators on a Hilbert or Banach space. Continuing …

Euclidian Geometry: Proposed Lesson Plans To Teach Throughout A One Semester Course, Joseph Willert

Mathematics Undergraduate Theses

Overview We provide several engaging lesson plans that would aid in the teaching of geometry, specifically targeting Euclidian Geometry, towards students of high school age. The audience of this piece would be high school or college students who have not yet had an introduction to geometry, but have completed the standard mathematical courses leading up to this point (i.e. algebra, elementary math, etc.). This being the case the lessons and concepts realized in Chapter 1 target a basic understanding of what Euclidian Geometry is and the subsequent chapters aim specifically at underlying properties of a geometry. The main source of …

Italian Domination On Ladders And Related Products, Bradley Gardner

Electronic Theses and Dissertations

An Italian dominating function on a graph $G = (V,E)$ is a function such that $f : V \to \{0,1,2\}$, and for each vertex $v \in V$ for which $f(v) = 0$, we have $\sum_{u\in N(v)}f(u) \geq 2$. The weight of an Italian dominating function is $f(V) = \sum_{v\in V(G)}f(v)$. The minimum weight of all such functions on a graph $G$ is called the Italian domination number of $G$. In this thesis, we will consider Italian domination in various types of products of a graph $G$ with the complete graph $K_2$. We will find the value of the Italian domination …

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms …

Pythagorean Theorem Area Proofs, Rachel Morley

Mathematics Undergraduate Theses

This composition is intended to walk the reader through four proofs of the pythagorean theorem that are based on area. It could be used in a classroom to solidify the pythagorean theorem after studying Neutral and Euclidean Geometries.

Topological Properties Of A 3-Rung Möbius Ladder, Rebecca Woods

Electronic Theses and Dissertations

In this work, we discuss the properties of the 3-rung Möbius ladder on the torus. We also prove ℤ₂ is an orientation preserving topological symmetry group of the 3-rung Möbius ladder with sides and rungs distinct, embedded in the torus.

Blow-Up Solutions Of Wave Map Equations With Periodic In Time Speed Of Propagation, Nathalie M. Luna-Rivera

Theses and Dissertations

We study the initial value problem for the wave map equation with time-dependent speed of propagation. In particular, for arbitrary, small, and smooth initial data we construct blow-up solutions of the wave map with coefficients that are periodic in time. For the proof we use Lyapunov-Floquet theory and Borg’s theorem.

Identities For Partitions Of N With Parts From A Finite Set, Acadia Larsen

Theses and Dissertations

We show for a prime power number of parts m that the first differences of partitions into at most m parts can be expressed as a non-negative linear combination of partitions into at most m – 1 parts. To show this relationship, we combine a quasipolynomial construction of p(n,m) with a new partition identity for a finite number of parts. We prove these results by providing combinatorial interpretations of the quasipolynomial of p(n,m) and the new partition identity. We extend these results by establishing conditions for when partitions of n with parts coming from …

Multi-Resolution Analysis Using Wavelet Basis Conditioned On Homogenization, Abibat Adebisi Lasisi

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This dissertation considers an approximation strategy using a wavelet reconstruction scheme for solving elliptic problems. The foci of the work are on (1) the approximate solution of differential equations using multiresolution analysis based on wavelet transforms and (2) the homogenization process for solving one and two-dimensional problems, to understand the solutions of second order elliptic problems. We employed homogenization to compute the average formula for permeability in a porous medium. The structure of the associated multiresolution analysis allows for the reconstruction of the approximate solution of the primary variable in the elliptic equation. Using a one-dimensional wavelet reconstruction algorithm proposed …

Generalized &Thetas;-Parameter Peakon Solutions For A Cubic Camassa-Holm Model, Michael Rippe

Theses and Dissertations

In this paper we outline a method for obtaining generalized peakon solutions for a cubic Camassa-Holm model originally introduced by Fokas (1995) and recently shown to have a Lax pair representation and bi-Hamiltonian structure by Qiao et al (2012). By considering an amended signum function—denoted sgn &thetas;(x)—where sgn(0) = &thetas; for a constant &thetas;, we explore new generalized peakon solutions for this model. In this context, all previous peakon solutions are of the case &thetas; = 0. Further, we aim to analyze the algebraic quadratic equation resulting from a substitution of the single-peakon ansatz equipped with our amended …

The Strong Law Of Large Numbers For U-Statistics Under Random Censorship, Jan Höft

Theses and Dissertations

We introduce a semi-parametric U-statistics estimator for randomly right censored data. We will study the strong law of large numbers for this estimator under proper assumptions about the conditional expectation of the censoring indicator with re- spect to the observed life times. Moreover we will conduct simulation studies, where the semi-parametric estimator is compared to a U-statistic based on the Kaplan- Meier product limit estimator in terms of bias, variance and mean squared error, under different censoring models.

Dynamic Pricing With Variable Order Sizes For A Model With Constant Demand Elasticity, Nyles Kirk Breecher

Theses and Dissertations

We investigate a dynamic pricing model under constant demand elasticity which accounts for customers ordering multiple items at once. A closed form expression for the optimal expected revenue and pricing strategy is found. Models with the same demand are shown to have asymptotically similar expected revenue and pricing strategies, even if the order size distributions of the customers are different. Surprisingly, the relative difference between comparable models is shown to be independent of time and the magnitude of demand. Variations of the model are considered, including different low inventory behavior as well as the effect of advertising. Some numerical simulations …

Triebel-Lizorkin Spaces Estimates For Evolution Equations With Structure Dissipation, Jingchun Chen

Theses and Dissertations

This work is concerned with the long time decay estimates of the generalized heat equations and the generalized wave equations in the homogeneous Triebel-Lizorkin spaces. We first extend the known results for the generalized heat equations in the real Hardy spaces. We also extend the known results for the generalized wave equations with structure dissipation in the real Hardy spaces.

The main tools employed are the decomposition of the unit, duality property in Triebel-Lizorkin spaces and the multiplier theorems in different function spaces such as Lebesgue spaces, real Hardy spaces and Triebel-Lizorkin spaces.

Hartogs Domains And The Diederich-Fornæss Index, Muhenned Abdulameer Abdulsahib

Graduate Theses and Dissertations

The Diederich-Fornss Index has played a crucial role in studying regularity of the Bergman projection on pseudoconvex domains in Sobolov spaces as is shown by Kohn, Harrington, Pinton and Zampieri and others. In this work, we discuss the Diederich-Fornss Index on Hartogs domains, and its relation to other properties connected to regularity of the Bergman projection. An upper and lower bound for the Diederich-Fornss Index is calculated for Hartogs domains and computed sharply for worm domains. Related conditions for the existence of a strong Stein neighborhood basis for Hartogs domains are introduced.

Scheduling Problems, Aamir Kudai

Honors Theses

Manufacturing industry is growing exponentially. The need of using algorithms and computational techniques to enhance processes is increasing every day. Algorithms help us solve almost all kind of computational problems. Not only choosing the right algorithm for a problem is important but also optimizing its time and space efficiency is crucial. BorgWarner Transmission Systems located in Water Valley, Mississippi is one among the leading manufacturing companies. This paper will demonstrate a real-world audit scheduling problem happened at BorgWarner and the techniques used to solve it. A gentle introduction to some of the heuristic algorithms such as Genetic algorithm, Randomized algorithm, …

Predicted Deepwater Bathymetry From Satellite Altimetry: Non-Fourier Transform Alternatives, Maxsimo Salazar

Dissertations

Robert Parker (1972) demonstrated the effectiveness of Fourier Transforms (FT) to compute gravitational potential anomalies caused by uneven, non-uniform layers of material. This important calculation relates the gravitational potential anomaly to sea-floor topography. As outlined by Sandwell and Smith (1997), a six-step procedure, utilizing the FT, then demonstrated how satellite altimetry measurements of marine geoid height are inverted into seafloor topography. However, FTs are not local in space and produce Gibb’s phenomenon around discontinuities. Seafloor features exhibit spatial locality and features such as seamounts and ridges often have sharp inclines. Initial tests compared the windowed-FT to wavelets in reconstruction of …

Exploring Flag Matroids And Duality, Zachary Garcia

Electronic Theses, Projects, and Dissertations

Matroids capture an abstraction of independence in mathematics, and in doing so, connect discrete mathematical structures that arise in a variety of contexts. A matroid can be defined in several cryptomorphic ways depending on which perspective of a matroid is most applicable to the given context. Among the many important concepts in matroid theory, the concept of matroid duality provides a powerful tool when addressing difficult problems. The usefulness of matroid duality stems from the fact that the dual of a matroid is itself a matroid. In this thesis, we explore a matroid-like object called a flag matroid. In particular, …

Symmetric Presentations And Double Coset Enumeration, Charles Seager

Electronic Theses, Projects, and Dissertations

In this project, we demonstrate our discovery of original symmetric presentations and constructions of important groups, including nonabelian simple groups, and groups that have these as factor groups. The target nonabelian simple groups include alternating, linear, and sporadic groups. We give isomorphism types for each finite homomorphic image that has been found. We present original symmetric presentations of $M_{12}$, $M_{21}:(2 \times 2)$, $L_{3}(4):2^2$, $2:^{\cdot}L_{3}(4):2$, $S(4,3)$, and $S_{7}$ as homomorphism images of the progenitors $2^{*20}$ $:$ $A_{5}$, $2^{*10}$ $:$ $PGL(2,9)$, $2^{*10}$ $:$ $Aut(A_{6})$, $2^{*10}$ $:$ $A_{6}$, $2^{*10}$ $:$ $A_{5}$, and $2^{*24}$ $:$ $S_{5}$, respectively. We also construct $M_{12}$, $M_{21}:(2 \times 2)$, …

Generalized Line Graphs, Mohra Abdullah Z. Alqahtani

Dissertations

With every nonempty graph, there are associated many graphs. One of the best known and most studied of these is the line graph L (G) of a graph G, whose vertices are the edges of G and where two vertices of L (G) are adjacent if the corresponding edges of G are adjacent. This concept was implicitly introduced by Whitney in 1932. Over the years, characterizations of graphs that are line graphs have been given, as well as graphs whose line graphs have some specified property. For example, Beineke characterized graphs that are line graphs by forbidding certain graphs …

The Mathematical Aspects Of Theoretical Physics, Hassan Kesserwani

Theses and Dissertations

The aim of this thesis is to outline the mathematical machinery of general relativity, quantum gravity, cosmology and an introduction to string theory under one body of work. We will flesh out tensor algebra and the formalism of differential geometry. After deriving the Einstein field equation, we will outline its traditional applications. We then linearize the field equation by a perturbation method and describe the mathematics of gravitational waves and their spherical harmonic analysis. We then transition into the derivation of the Schwarzschild metric and the Kruskal coordinate transformation, in order to set the stage for quantum gravity. This sets …

Contact Numbers For Packing Of Spherical Particles, Eduardo Alejandro Ramirez Martinez

Theses and Dissertations

This thesis covers packings of spherical particles. The main object of this investigation is the contact number of a packing. New bounds for contact numbers of certain families of sphere packings in dimension 3 are obtained as the outcome of this research.

Asymptotic Quantization For A Condensation System Associated With A Discrete Distribution, Shankar Parajulee

Theses and Dissertations

Let P := (1/3)P ○ S1–1 + (1/3)P ○ S2–1 + (1/3)v be a condensation measure on R, where S1(x) = (1/5)x, S2(x) = (1/5)x + 4/5 for all x ∈ R , and v is a discrete distribution on R with the support of v equals C := {(2/5), (3/5)}. For such a measure P we determine the optimal sets of n–means and the nth quantization errors for all n ≥ 2. In addition, we show that the quantization dimension of the condensation measure P exists and equals …

Group Theory And Particles, Elizabeth V. Hawkins

Honors College Theses

We begin by a brief overview of the notion of groups and Lie groups. We then explain what group representations are and give their main properties. Finally, we show how group representation form a natural framework to understand the Standard Model of physics.

The Compensation For Few Clusters In Clustered Randomized Trials With Binary Outcomes, Lily Stalter

Mathematics & Statistics ETDs

Cluster randomized trials are increasingly popular in epidemiological and medical research. When analyzing the data from such studies it is imperative that the hierarchical structure of the data be taken into account. Multilevel logistic regression is used to analyze clustered data with binary outcomes. Previous literature shows that a greater number of clusters is more important than a large number of subjects per cluster. This paper investigates if it is possible to compensate for the increased bias found for parameter estimates when the number of clusters is decreased. A simulation study was conducted where the absolute percent relative bias for …

A Complete Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder Genannt Luehr

Doctoral Dissertations

A graph is outer-planar (OP) if it has a plane embedding in which all of the vertices lie on the boundary of the outer face. A graph is near outer-planar (NOP) if it is edgeless or has an edge whose deletion results in an outer-planar graph. An edge of a non outer-planar graph whose removal results in an outer-planar graph is a vulnerable edge. This dissertation focuses on near outer-planar (NOP) graphs. We describe the class of all such graphs in terms of a finite list of excluded graphs, in a manner similar to the well-known Kuratowski Theorem for planar …